Abstract
We present a tool for automated theorem proving in Agda, an implementation of Martin-Löf’s intuitionistic type theory. The tool is intended to facilitate interactive proving by relieving the user from filling in simple but tedious parts of a proof. The proof search is conducted directly in type theory and produces proof terms. Any proof term is verified by the Agda type-checker, which ensures soundness of the tool. Some effort has been spent on trying to produce human readable results, which allows the user to examine the generated proofs. We have tested the tool on examples mainly in the area of (functional) program verification. Most examples we have considered contain induction, and some contain generalisation. The contribution of this work outside the Agda community is to extend the experience of automated proof for intuitionistic type theory.
Research supported by the project Cover of the Swedish Foundation of Strategic Research (SSF).
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References
Abel, A., Coquand, T., Norell, U.: Connecting a logical framework to a first-order logic prover (2005) (submitted)
Andrews, P.B.: Classical type theory. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. 2, ch. 15, pp. 965–1007. Elsevier Science, Amsterdam (2001)
Coquand, C.: The AGDA Proof System Homepage (1998), http://www.cs.chalmers.se/~catarina/agda/
Cornes, C.: Conception d’un langage de haut niveau de représentation de preuves: Récurrence par filtrage de motifs, Unification en présence de types inductifs primitifs, Synthèse de lemmes d’inversion. PhD thesis, Université Paris 7 (1997)
Dowek, G.: A complete proof synthesis method for the cube of type systems. J. Logic and Computation 3(3), 287–315 (1993)
Dowek, G.: Higher-order unification and matching. In: Robinson, A., Voronkov, A. (eds.) Handbook of automated reasoning, vol. 2, ch. 16, pp. 1009–1062. Elsevier Science, Amsterdam (2001)
Dybjer, P.: Inductive sets and families in martin-löf’s type theory and their set-theoretic semantics. In: Logical frameworks, pp. 280–306. Cambridge University Press, New York (1991)
Lindblad, F.: Agsy problem examples (2004), http://www.cs.chalmers.se/~frelindb/Agsy_examples.tgz
Magnusson, L.: The Implementation of ALF - a Proof Editor based on Martin-Löf’s Monomorphic Type Theory with Explicit Substitution. PhD thesis, Department of Computing Science, Chalmers University of Technology and University of Göteborg (1994)
Martin-Löf, P.: Intuitionistic Type Theory. Bibliopolis, Napoli (1984)
Schürmann, C., Pfenning, F.: Automated theorem proving in a simple meta-logic for LF. In: Kirchner, C., Kirchner, H. (eds.) CADE 1998. LNCS (LNAI), vol. 1421, pp. 286–300. Springer, Heidelberg (1998)
Tammet, T., Smith, J.: Optimized encodings of fragments of type theory in first-order logic. Journal of Logic and Computation 8 (1998)
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Lindblad, F., Benke, M. (2006). A Tool for Automated Theorem Proving in Agda. In: Filliâtre, JC., Paulin-Mohring, C., Werner, B. (eds) Types for Proofs and Programs. TYPES 2004. Lecture Notes in Computer Science, vol 3839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11617990_10
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DOI: https://doi.org/10.1007/11617990_10
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